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The flow tree formula for Donaldson–Thomas invariants of quivers with potentials

Part of: Projective and enumerative geometry Representation theory of rings and algebras

Published online by Cambridge University Press:  19 December 2022

Hülya Argüz  and
Pierrick Bousseau
Hülya Argüz
Affiliation:
University of Georgia, Department of Mathematics, Athens, GA 30605, USA hulya.arguz@uga.edu
Pierrick Bousseau
Affiliation:
University of Georgia, Department of Mathematics, Athens, GA 30605, USA pierrick.bousseau@uga.edu
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Abstract

We prove the flow tree formula conjectured by Alexandrov and Pioline, which computes Donaldson–Thomas invariants of quivers with potentials in terms of a smaller set of attractor invariants. This result is obtained as a particular case of a more general flow tree formula reconstructing a consistent scattering diagram from its initial walls.

Keywords

quiver representationsDonaldson–Thomas invariantsscattering diagrams

MSC classification

Primary: 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants 16G20: Representations of quivers and partially ordered sets
Type
Research Article
Information
Compositio Mathematica , Volume 158 , Issue 12 , December 2022 , pp. 2206 - 2249
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Copyright
© 2022 The Author(s). The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence

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